The two were on the lake in a Zodiac dinghy when Mrs Letts-Beckett went into the water.
"I was sitting with my back to her and she was sitting with her front to me, I think," Mr Beckett told Royal Canadian Mounted Police Constable Jennifer Perrault in a thick New Zealand accent.
"The last I can remember, she said that her back was sore. And then, all of a sudden, there's a splash. I think she stood up to stretch her back."
Mr Beckett told the investigator he was fishing and his wife was eating an apple and chips while holding an umbrella for shade. He said she had taken off her life jacket because she felt hot. He described her as "a fair-weather sailor" who does not swim.
"She was still holding the umbrella and she fell over the side," he said. "The umbrella was over the other side. She kind of went down the side of the boat."
Mr Beckett said he could see his wife drifting farther away from him in the water.
"Then I spun the boat around to look for her and I could see her under the water," he said. "I went over the side of the boat, but I couldn't get down far enough."
In the statement, Mr Beckett said Mrs Letts-Beckett was 15 to 20 feet beneath the surface.
"I could see her, but ... couldn't reach her," he said. "So, I went to shore and got a rock and swam out, but I couldn't find her then. Then I saw some bubbles."
Mr Beckett said he used the rock to get far enough underwater to grab his wife by the hand and pull her to the surface.
"As I was swimming to shore, I was blowing air into her lungs, into her mouth, trying to do CPR," he said.
After performing chest compressions on shore, Mr Beckett said, he swam out to retrieve his boat and tried unsuccessfully to lift his wife on board.
He said he then decided to drive to a nearby pontoon boat to ask for help.
John Saharchuk told the court he drove his pontoon boat to where Beckett said he left his wife.
"I went right over to her," Mr Saharchuk said. "It looked to me like she was very much dead at that point -- the colour of her face and everything."
After attempting further CPR, Mr Beckett and Mr Saharchuk loaded Mrs Letts-Beckett's body into the pontoon boat and returned to the Shelter Bay campsite, where they were staying.
On shore, Mr Saharchuk said, an off-duty paramedic confirmed Mrs Letts-Beckett was dead.
Mr Beckett, formerly a city councillor in Napier, moved to Canada in 2000 to be closer to Mrs Letts-Beckett. The two had met five years earlier. The couple wed in 2003 and lived in Westlock, Alberta, where Mrs Letts-Beckett worked as a schoolteacher.
Mr Beckett's trial is expected to last three months.